Respuesta :
Answer:
$3,979.
Explanation:
Interest can be described as the cost of borrowing. This means that the amount that is paid for using money borrowed from a bank or other financial institutions is called interest.
Interest can be ordinary interest or exact interest. When the estimation of an interest is done on the basis of of a 360-day year, it is called ordinary interest. But when the estimation of an interest is done on the basis of of a 365-day year, it is called exact interest.
The formula for calculating both ordinary and exact interests is the same, but it just the days has to be adjusted. The general formula is given as follows:
I = Prt ............................................................. (1)
Where,
P = principal borrowed = ?
r = interest rate = 9.75% = 0.0975
t = time expressed in years = 254
Equation (1) can be therefore be amended for days for ordinary interest as follows:
OI = Pr (D/360) .............................................. (2)
Where
OI = ordinary interest
D = number of days = 254
D/360 = t for ordinary interest
Equation (1) can also be be amended for days for exact interest as follows:
OI = Pr (D/365) .............................................. (3)
Where
OI = ordinary interest = $270
D = number of days = 254
D/365 = t for exact interest
Since the asked to use the exact method, we therefore use equation (3), substitute all the relevant value into it and solve for P as follows:
270 = P × 0.0975 × (254 ÷ 365)
270 = P × 0.0975 × 0.695890410958904
270 = P × 0.0975 × 0.695890410958904
270 = P × 0.0678493150684931
P = 270 ÷ 0.0678493150684931
P = 3,979.4064203513
P = $3,979 (rounded to the nearest whole dollar amount)
Therefore, the amount of principal borrowed is $3,979.
